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Compatibility of state assignments and pooling of information

Todd A. Brun, Min-Hsiu Hsieh, and Christopher Perry
Phys. Rev. A 92, 012107 – Published 13 July 2015

Abstract

We say that two (or more) state assignments for one and the same quantum system are compatible if they could represent the assignments of observers with differing information about the system. A criterion for compatibility was proposed in [Phys. Rev. A 65, 032315 (2002)]; however, this leaves unanswered the question of whether there are degrees of compatibility which could be represented by some quantitative measure, and whether there is a straightforward procedure whereby the observers can pool their information to arrive at a unique joint state assignment. We argue that such measures are only sensible given some assumption about what kind of information was used in making the state assignments in the first place, and that in general state assignments do not represent all of the information possessed by the observers. However, we examine one particular measure and show that it has a straightforward interpretation, assuming that the information was acquired from a particular type of measurement, and that in this case there is a natural rule for pooling information. We extend this measure to compatibility of states for k observers and show that the value is the solution to a semidefinite program. Similar compatibility measures can be defined for alternative notions of state compatibility, including post-Peierls and equal support compatibilities.

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  • Received 20 April 2015

DOI:https://doi.org/10.1103/PhysRevA.92.012107

©2015 American Physical Society

Authors & Affiliations

Todd A. Brun*

  • Communication Sciences Institute, University of Southern California, Los Angeles, California 90089, USA

Min-Hsiu Hsieh

  • Centre for Quantum Computation & Intelligent Systems (QCIS), Faculty of Engineering and Information Technology, University of Technology, Sydney NSW 2007, Australia

Christopher Perry

  • Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom

  • *tbrun@usc.edu
  • min-hsiu.hsieh@uts.edu.au
  • christopher.perry.12@ucl.ac.uk

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Issue

Vol. 92, Iss. 1 — July 2015

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